Will players still sign for City

After the shenanigans of the Lampard deal it has emerged he actually signed for CFG. I assume this is the City Football Group which encompasses all teams.
Will players who we sign do so for CFG meaning they can be loaned out to other sides if necessary? Like Lampard for example. Or was this a one off and players will sign for MCFC as they have previously done. It would make sense for some signings, if not all, to sign for CFG as we as the parent club can decide where best to send/play them without any restrictions or comebacks on loan deals. There may be commercial reasons for this as well.
Thoughts?
Will players who we sign do so for CFG meaning they can be loaned out to other sides if necessary? Like Lampard for example. Or was this a one off and players will sign for MCFC as they have previously done. It would make sense for some signings, if not all, to sign for CFG as we as the parent club can decide where best to send/play them without any restrictions or comebacks on loan deals. There may be commercial reasons for this as well.
Thoughts?